{
  "id": 4193,
  "curve_key": "81306531572465881242576:-21475974081777031627312174494770880",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1693886074426372525887",
    "24856451483538231050129831591170"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "naive_height": 158.2575399160393,
  "faltings_height": 11.146688317608737,
  "conductor": "16727690052741601039120629516045392048387642326599525010968",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "144981901",
    "48511425331",
    "171842641613",
    "48950125555422649693799"
  ],
  "discriminant": "44143437298542131612581150537590891073740278391925856930543937792",
  "regulator": "57045721336677772.164147602315923431764054067867067913400278010908392793731",
  "points": [
    [
      "-1937770540187659/241081",
      "-729228678078715512198798/118370771"
    ],
    [
      "46826439778337/49",
      "320139873797186393742/343"
    ],
    [
      "-464077505655639/58564",
      "-87113753550275506819933/14172488"
    ],
    [
      "-38015202003",
      "-5857643839199702"
    ],
    [
      "3966036693977/256",
      "-6255704023786339683/4096"
    ],
    [
      "-141282972491093/3969",
      "-1582382897791898520032/250047"
    ],
    [
      "18278551835",
      "-40385480800920"
    ],
    [
      "-24903800240952537/737881",
      "-4184351182803945334839224/633839779"
    ],
    [
      "360518603815/9",
      "-124552816313710400/27"
    ],
    [
      "-16836223248042/529",
      "-82993756697801919284/12167"
    ],
    [
      "200560085013857/961",
      "-2788496862357887367918/29791"
    ],
    [
      "969904941722",
      "-954351430695210702"
    ],
    [
      "-716481906953338/39601",
      "-55490121394639847082552/7880599"
    ],
    [
      "-1069634837200604299/80694289",
      "-4861569708671506896767519202/724876798087"
    ],
    [
      "23110412809931/2209",
      "-298754305107375421392/103823"
    ],
    [
      "-36380946623837/4761",
      "-2007778653622532274904/328509"
    ],
    [
      "-5087789795233239/303601",
      "-1165438315177648174142438/167284151"
    ],
    [
      "30016824379421/2209",
      "-216496465017366751098/103823"
    ]
  ],
  "submitter": "Andrii Prokhorenkov",
  "history": [],
  "commentary": "Mestre rank-12 quartic family on locus sextuple [0,14,790,819,859,920] at T=491 (y^2=(g^2-p(x-T)p(x+T))/T^2, Jacobian); 18 independent points from a quartic rational-point search.",
  "created_at": "2026-10-12 04:10:17",
  "updated_at": "2026-10-12 04:10:17"
}